A $7\mathrm{.}5-hp,120-V$ series de motor has an armature resistance of $0\mathrm{.}2$ and a series field resistance of $0\mathrm{.}1236.$ At full load, the current input is $60$ A $,$ and the rated $($full load$)$ speed is $1050\frac{r}{m}in.$ Assume its magnetization curve is linear. The core losses are $200$ W $,$ and the mechanical are $240$ W at full load. Assume that the mechanical losses vary as the cube of the speed of the motor and the core losses are constant. $($Ignore stray losses and brush voltage drop losses$)$ Find;

a$)$ Efficiency of the motor at full load $(5$ P$)$

b$)$ Induced torque at full load $(5$P$)$

c$)$ Internal generated voltage at full load, $E_A(5$P$)$

d$)$ Speed and efficiency of the motor if it is operating at an input current of $35$ A $(15$ P$)$

$1hp=746W$